Large-Scale Estimation under Unknown Heteroskedasticity

Fuente: arXiv
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Main Author: Ho, Sheng Chao
Format: Preprint
Published: 2025
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author Ho, Sheng Chao
author_facet Ho, Sheng Chao
contents This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of heterogeneous parameters, such as unit-specific means or quantiles, in terms of the density of certain sufficient statistics. These are used to propose feasible versions with nearly parametric regret bounds of the order of $(\log n)^κ/ n$. The estimators are employed in a study of teachers' value-added, where we find that allowing for heterogeneous variances across teachers is crucial for delivery optimal estimates of teacher quality and detecting low-performing teachers.
format Preprint
id arxiv_https___arxiv_org_abs_2507_02293
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Large-Scale Estimation under Unknown Heteroskedasticity
Ho, Sheng Chao
Econometrics
This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of heterogeneous parameters, such as unit-specific means or quantiles, in terms of the density of certain sufficient statistics. These are used to propose feasible versions with nearly parametric regret bounds of the order of $(\log n)^κ/ n$. The estimators are employed in a study of teachers' value-added, where we find that allowing for heterogeneous variances across teachers is crucial for delivery optimal estimates of teacher quality and detecting low-performing teachers.
title Large-Scale Estimation under Unknown Heteroskedasticity
topic Econometrics
url https://arxiv.org/abs/2507.02293